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**Unformatted text preview: **n—rqu-qh. — n;m-t.~..—m-myu-.~s. .. 6.10 64! Bl‘osrarzotzm Hw 500mm
HWS 6.10 5.0 6.!) 6.15 6ng 6.17 Exercise 10 a. The probability that the principal source of payment is private insurance is 0.387.
b. Since the sources of payment are all mutually exclusive, the probability that the principal source of payment is Medicare, Medicaid, or some other government program is
P(Medicare or Medicaid or other) = P(Medicare) + P(Medicaid) + P(other)
= 0.345 + 0.116 + 0.033
= 0.494. c. Given that the principal source of payment is a government program, the probability that it
is Medicare is P(Medicare and government program)
P(governrnent program)
P(Medicare)
P(gcwernment program)
0.345
0.494
0.698. ll P(Medicare I government program) Exercise 11
a. Since these events are independent, the probability that both adults are uninsured is P(both uninsured) = P(wornan uninsured) x P(man uninsured)
0.123 X 0.123
0.015. b. The probability that both adults are insured is P(both insured) = (1 — 0.123) x (1 — 0.123)
= 0.877 x 0.377
= 0.709. c. The probability that all ﬁve adults are uninsured is 0.123 x 0.123 x 0.123 x 0.123 x 0.123
= 0.000028. 6"} Exercise 13
a. The probability of a. false negative result is
P(—- test { ca.) = 1 — sensitivity
1 — 0.85
0.15. H b. The probability of a false positive result is P(+ test | no ca) = 1 — speciﬁcity
= 1 — 0.80
= 0.20. i
! c. Since P(ca.) = 0.0025 and P(no ca) = 0.9975, the probability that a woman has breast cancer
1 - given that her mammogram is positive is P(ca)P(+ test I ca.)
P(ca)P(+ test [ ca) + P(no ca)P(+ test | noca) (0.0025)(0.85)
(0.0025)(0.85) + (o.9975)(o.20) 0.0105. P(ca l + test) = 6, '5 Exercise 15
a. The sensitivity of radionuclide ventriculography is 302
481 *
0.628, P(+rv \ cad) ll and its speciﬁcity is 313
452
= 0.823. P(—rv I no cad) b. Since P(cad) = 0.10 and P(no cad) = 0.90, the probability that an individual has coronary
artery disease given that he or she tests positive is P(+rv [ cad)P(cad)
P(+rv I cad)P(cad) + P(+rv i no cad)P(no cad) (0;628)(0.10)
(0.628)(0.10) + (0.177)(0.90) = 0.283. P(cad I +rv) c. The predictive value of a negative test is
‘ P(—rv 1 no cad)P(no cad)
P(—rv | no cad)P(no cad) + P(—rv l cad)P(cad) (0.823)(0.90)
(0.823)(0.90) + (o.372)(o.10) 0.952. P(no cad | —rv) = usumxmmnmm vvmurvaemmumn maummmﬂmmmmmmwmmvwmﬂmﬂ s:unu,:-n~w>\n mm‘ua‘rvk‘l a 648 647 Exercise 18 The relative risk of pregnancy for women using a particular contraceptive method versus
women not using any type of protection is calculated as RR P(pregnancy | method)
P(pregnancy I no protection) P(pregnancy f method)
0.431 ' Note that each of the relative risks below takes a value less than 1, indicating that each of the methods carries a lower risk of pregnancy than no protection at all. The Pill has the smallst
relative risk (least risk, relative to no protection), and the diaphragm the largest. Method of
Contraception Relative
Risk . Diaphragm 0.346
Condom 0.246
IUD 0. 165
Pill 0. 086 Exercise 19. a. The probabilities of suﬂ'ering from persistent respiratory symptoms by socioeconomic status
are shown below. Socioeconomic Status Probability Low 0.392
Middle 0.238
High 0.141 b. Let 5’ represent the presence of symptoms. The odds of experiencing persistent respiratory
symptoms for the middle group relative to the high group are P(S l middle) /[1 — P(S | middle)]
P(S | high) /[1 — P(S’ I high)] (0.238) /(1 — 0.238)
(0.141)/(1 — 0.141) = 1.90, OR: I! and for the low group relative to the high group are
P(S | low)/[1— P(S | low)]
P(5 | hish)/[1 - P(5 I high” (0.392) /(1 — 0.392)
(0.141) /(1 — 0.141) = 3.93. OR c. There does appear to be an association between socioeconomic status and respiratory
symptom; the odds of experiencing symptoms increase as socioeconomic status decreases. ...

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- Summer '15
- AlexandraNica
- Statistics, Biostatistics, Mutually Exclusive, Probability, Type I and type II errors, government program